Principal Component Analysis(PCA)

Principal Component Analysis(PCA)

Principal Component Analysis(PCA) Principal Component Analysis (PCA) is an unsupervised machine learning feature reduction technique for high-dimensional and correlated data sets. Images and text documents have high dimensional data sets which requires unnecessary computation power and storage. Basic goal of PCA is to select features which have high variance. High variance of a feature indicates … Read more Principal Component Analysis(PCA)

Logistic Regression

Logistic Distribution PDF

Hyperbolic Functions These functions are very important in regression, classification and to build neural networks. Moreover, it is important to remember expression hyperbolic functions in the form of exponential functions. I have written the expressions and plotted the functions using python library. Python Codes to Plot Hyperbolic Functions import numpy as np import matplotlib.pyplot as … Read more Logistic Regression

Linear Regression in Statistics

Calculation-for-Regression-Line

Linear regression Linear regression refers to find out degree of relationship between two variables in the form of a linear function y=mx+c using statistical techniques. Where m is gradient and c is intercept on y axis. That best fits the data set, which predicts the value of y for a given x or vice versa. … Read more Linear Regression in Statistics

Poisson Distribution as a Limiting Case of Binomial Distribution

For large value of n binomial distribution asymptotically tends to Poisson distribution. Probability distribution  function of binomial random variable  is Probability distribution of Poisson random variable is Poisson Distribution as a Limiting Case of Binomial Distribution Python Code for Binomial Distribution from scipy.stats import binom import numpy as np import matplotlib.pyplot as plt # Let … Read more Poisson Distribution as a Limiting Case of Binomial Distribution

Exponential Probability Distribution

Mean of Exponentially Distributed Random Variable X

A random variable X is said to follow exponential distribution if it follows the following probability mass function. Exponential probability distribution is a continuous distribution. Probability Distribution Function of Exponentially Distributed Variable X   It is heavily used in the Internet traffic modelling and of study queuing models. Numerical Example- Problem- If a computer receives … Read more Exponential Probability Distribution

Central Limit Theorem and Normal Distribution

Area Under Normal Distribution Curve

  Why is normal distribution is important? To understand the question you have to go through the Central Limit Theorem. Central Limit Theorem According to central limit theorem if X1, X2, X3,……Xn are random variables drawn from any probability distribution function with mean  Σμi  and standard deviation Σσi where (i=1,2,3,……n). The sum of random variables … Read more Central Limit Theorem and Normal Distribution

Correlation in Statistics

Spearman Rank Correlation

Correlation Correlation measures  the relation between two variables  that how they are related.  And is denoted by r and  ρ moreover, the correlation quantifies the level of relationship between -1 to +1. If the value of correlation  r is -1 then there is perfect negative relationship. If value of  correlation is  +1  then there is … Read more Correlation in Statistics

Standard Deviation, Variance and Covariance

Standard Deviation

Standard Deviation Variance and Covariance Standard deviation, variance and covariance have very important applications in machine learning and data science. Further, they are closely related to each other. In feature reduction techniques, such as PCA ( Principle Component Analysis) features are selected based on  high variance.  In this post I will explain standard deviation, variance … Read more Standard Deviation, Variance and Covariance

Skewness and Kurtosis

Skewness and Kurtosis- Introduction- Skewness and Kurtosis are very important  concepts in statistics and have several applications.  In addition, they characterize the nature of data distribution which make data analysis easier. Moreover, I will separately discuss skewness and kurtosis in further sections. Skewness- Skewness  refers the measurement of lack of symmetry in data distribution. Measures … Read more Skewness and Kurtosis

CSIR-NET Syllabus for Mathematical Sciences

csirnet math syllabus

CSIR-UGC National Eligibility Test (NET) for Junior Research Fellowship and Lecturer-ship COMMON SYLLABUS FOR PART ‘B’ AND ‘C’ MATHEMATICAL SCIENCES UNIT –  1 Analysis: Elementary set theory, finite, countable and uncountable sets, Real number system as a complete ordered field, Archimedean property, supremum, infimum. Sequences and series, convergence, limsup, liminf. Bolzano Weierstrass theorem, Heine Borel … Read more CSIR-NET Syllabus for Mathematical Sciences